Question

In one state lottery​ game, you must select four digits​ (digits may be​ repeated). If your number matches exactly the four digits selected by the lottery​ commission, you win.

​1) How many different numbers may be​ chosen?
​2) If you purchase one lottery​ ticket, what is your chance of​ winning?
​3) There are ___ different numbers that can be chosen. ​(Type a whole​ number.)
​4) There is a ___ chance of winning.*

*The answer choices for number 4 are:
1 in 10,000
1 in 6,561
1 in 100
1 in 1,000
1 in 9,999

Answer 1

Part 1)

10,000 different numbers.

Part 2)

A) 1 in 10,000.

Explanation:

Part 1)

Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:

`T=\underbrace{10}_{\text{Choices For First Digit}}*\underbrace{10}_{\text{Second Digit}}*\underbrace{10}_{\text{Third Digit}}* \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000`

Thus, 10,000 different numbers are possible.

Part 2)

Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.

This is equivalent to 0.0001 or a 0.01% chance of winning.